Nevanlinna Theory of Meromorphic Functions
The value distribution theory of meromorphic functions on C established by R. Nevanlinna in 1925 is described. It not only deepened complex function theory in one variable but also led to the covering theory by L. Ahlfors and the value distribution theory in several complex variables. The aim of this chapter is to introduce the most fundamental part of the theory in a self-contained manner. We try to give the proofs by making use of those by H.L. Selberg and H. Cartan so that they are straightforward and compatible with those in the case of several complex variables presented in the later chapters.
KeywordsLine Bundle Entire Function Meromorphic Function Zeta Function Theta Function
- Beiträge zur Theorie der meromorphen Funktionen, 7e Congr. Math. Scand., Oslo, 1929, pp. 84–88, Oslo, 1930. Google Scholar
Carlson, J. and Griffiths, P.
Griffiths, P. and King, J.
- Modern Function Theory I (in Japanese), Morikita Publ. Co., Tokyo, 1976. Google Scholar